Leonidas S. Pitsoulis

Pareto Optimality, Game Theory and Equilibria

Part I Game and Game Theory.- Minimax: Existence and Stability.- Recent Advances in Minimax Theory and Applications.- On Noncooperative Games, Minimax Theorems and Equilibrium Problems.- Nonlinear Games.- Scalar Asymptotic Contractivity and Fixed-Points for Nonexpansive Mappings on Unbounded Sets.- Cooperative Combinatorial Games.- Algorithmic Cooperative Game Theory.- A Survey of Bicooperative Game Theory.- Cost Allocation in Combinatorial Optimization Games.- Time-Dependent Equilibrium Problems.- Differential Games of Multiple Agents and Geometrical Structures.- Convexity in Differential Games.- Game Dynamic Problems for Systems with Fractional Derivatives.- Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure.- Strategic Audit Policies Without Commitment.- Optimality and Efficiency in Auctions Design: A Survey.- Part II Multiobjective, KKT, Bilevel.- Solution Concepts and an Approximation Kuhn-Tucker Approach for Fuzzy Multi-Objective Linear Bilevel Programming.- Pareto Optimality.- Multiobjective Optimization: A Brief Overview.- Parametric Multiobjective Optimization.- Part III Applications.- The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems.- Traffic Assignmetn: Equilibrium Models.- Investment Paradoxes in Electricity Networks.- Algorithms for Network Interdiction and Fortification Games.- Game Theoretical Approaches in Wireless Networks.- A Military Application of Viability: Winning Cones, Differential Inclusions and Lanchester Type Models for Combat.- Statics and Dynamics of Global Supply Chain Networks.- Game Theory Models and Their Applications in Inventory Management in Supply Chain.

Algorithm 769: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP

In the NP-complete quadratic assignment problem (QAP), <italic>n</italic> facilities are to be assigned to <italic>n</italic> sites at minimum cost. The contribution of assigning facility <italic>i</italic> to site <italic>k</italic> and facility <italic>j</italic> to site <italic>l</italic> to the total cost is <italic>f<subscrpt>ij</subscrpt></italic> <italic>d<subscrpt>kl</subscrpt></italic>, where <italic>f<subscrpt>ij</subscrpt></italic> is the flow between facilities <italic>i</italic> and <italic>j</italic>, and <italic>d<subscrpt>kl</subscrpt></italic> is the distance between sites <italic>k</italic> and <italic>l</italic>. Only very small (<italic>n</italic>≤20) instances of the QAP have been solved exactly, and heuristics are therefore used to produce approximate solutions. This article describes a set of Fortran subroutines to find approximate solutions to dense quadratic assignment problems, having at least one symmetric flow or distance matrix. A greedy, randomized, adaptive search procedure (GRASP) is used to produce the solutions. The design and implementation of the code are described in detail, and extensive computational experiments are reported, illustrating solution quality as a function of running time.

Parallel Search for Combinatorial Optimization: Genetic Algorithms, Simulated Annealing, Tabu Search and GRASP

In this paper, we review parallel search techniques for approximating the global optimal solution of combinatorial optimization problems. Recent developments on parallel implementation of genetic algorithms, simulated annealing, tabu search, and greedy randomized adaptive search procedures (GRASP) are discussed.

A Parallel Grasp Implementation for the Quadratic Assignment Problem

In this paper we present a parallel implementation of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions to the quadratic assignment problem. In particular, we discuss efficient techniques for large-scale sparse quadratic assignment problems on an MIMD parallel computer. We report computational experience on a collection of quadratic assignment problems. The code was run on a Kendall Square Research KSR-1 parallel computer, using 1, 4, 14, 24, 34, 44, 54, and 64 processors, and achieves an average speedup that is almost linear in the number of processors.

A GRASP for the biquadratic assignment problem

The biquadratic assignment problem (BiQAP) is a generalization of the quadratic assignment problem (QAP). It is a nonlinear integer programming problem where the objective function is a fourth degree multivariable polynomial and the feasible domain is the assignment polytope. BiQAP problems appear in VLSI synthesis. Due to the difficulty of this problem, only heuristic solution approaches have been proposed. In this paper, we propose a new heuristic for the BiQAP, a greedy randomized adaptive search procedure (GRASP). Computational results on instances described in the literature indicate that this procedure consistently finds better solutions than previously described algorithms.

A Parallel Grasp for the Data Association Multidimensional Assignment Problem

Data association multidimensional assignment problems appear in many applications such as MultiTarget MultiSensor Tracking, and particle tracking. The problem is characterized by the large input data and is very difficult to solve exactly. A Greedy Randomized Adaptive Search Procedure (GRASP) has been developed and computational results show good quality solutions can be obtained. Furthermore, the efficiency of the GRASP can be easily improved by parallelization of the code in the MPI environment.

A Parallel GRASP for MAX-SAT Problems

The weighted maximum satisfiability (MAX-SAT) problem is central in mathematical logic, computing theory, and many industrial applications. In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for solving MAX-SAT problems. Experimental results indicate that almost linear speedup is achieved.

GRASP with path relinking for the weighted MAXSAT problem

A GRASP with path relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multistart metaheuristic, where, at each iteration, locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path relinking) and the GRASP with path relinking illustrates the effectiveness of path relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem.

Fortran subroutines for computing approximate solutions of weighted MAX-SAT problems using GRASP

Abstract This paper describes Fortran subroutines for computing approximate solutions to the weighted MAX-SAT problem using a greedy randomized adaptive search procedure (GRASP). The algorithm (Resende, Pitsoulis, and Pardalos, in: D.Z. Du et al. (Ed.), Satisfiability problem: Theory and Applications, Vol. 35 DIMACS Series on Discrete Mathametics and Theoretical Computer Science, American Mathematical Society, Providence, RI, 1997, pp. 393–405) is briefly outlined and its implementation is discussed. Usage of the subroutines is considered in detail. The subroutines are tested on a set of test problems, illustrating the tradeoff between running time and solution quality.

Community detection by modularity maximization using GRASP with path relinking

Complex systems in diverse areas such as biology, sociology and physics are frequently being modelled as graphs, that provide the mathematical framework upon which small scale dynamics between the fundamental elements of the system can reveal large scale system behavior. Community structure in a graph is an important large scale characteristic, and can be described as a natural division of the vertices into densely connected groups, or clusters. Detection of community structure remains up to this date a computationally challenging problem despite the efforts of many researchers from various scientific fields in the past few years. The modularity value of a set of vertex clusters in a graph is a widely used quality measure for community structure, and the relating problem of finding a partition of the vertices into clusters such that the corresponding modularity is maximized is an NP-Hard problem. In this paper we present a Greedy Randomized Adaptive Search Procedure (GRASP) with path relinking, for solving the modularity maximization problem in weighted graphs. A class of {0,1} matrices is introduced that characterizes the family of clusterings in a graph, and a distance function is given that enables us to define an l-neighborhood local search, which generalizes most of the related local search methods that have appeared in the literature. Computational experiments comparing the proposed algorithm with other heuristics from the literature in a set of artificially generated graphs and some well known benchmark instances, indicate that our implementation of GRASP with path relinking consistently produces better quality solutions.